Rromani people have South Asian admixture.
Since you do not have South Asian admixture is quite clear you have no Rromani/Indian ancestry.
H-M82 is not Rromani haplogroup only.
H-M82/H1a is also present in small percentages at Iranian people.
https://en.wikipedia.org/wiki/Haplogroup_H_(Y-DNA)#Distribution_of_H1a1-M82_and_H2-P96
You also have Iranic admixture.
So the origin of your H1a/H-M82 is of Iranic ancestry.
How Iranic ancestry got in Greece?
Lots of possible sources, if you read the history.
See that 2% of Macedonian Greeks also carries H-M82.
I also see you cluster 2nd closest to Macedonian Greeks on K16.
You are sure that your father is not Macedonian Greek?
How H-M82 got at Macedonian Greeks?
From Iranic people very likely,or from Indian people,Alexander the Great conquered also India etc.